Imagine an encryption scheme where it is possible to add and multiply numbers without any knowledge of the numbers. Instead one could manipulate encryptions of the numbers and then the decryption of the result would give the result of the arithmetic on the original numbers. Encryption algorithms with this property are called homomorphic and have various applications in cloud computing. Homomorphic encryption schemes exist but are generally so inefficient that they are not practical. This report introduces a toy cryptosystem called Bubbles: a somewhat homomorphic encryption scheme created by Professor Martin and Professor Sunar at Worcester Polytechnic Institute. We will show that the original scheme is insecure and may be efficiently "popped". We will then examine two variations of the scheme that introduce noise to increase security and show that Bubbles is still vulnerable except when parameters are carefully chosen. However these safe parameter choices make Bubbles more inefficient than other recent homomorphic schemes.
Worcester Polytechnic Institute
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Steele, Corre, "Popping Bubbles: Cryptanalysis of Homomorphic Encryption" (2016). Masters Theses (All Theses, All Years). 453.
homomorphic encryption, cryptanalysis